Other plum ties in the round of 16 see Wolfsburg host Inter Milan, Napoli welcome Dynamo Moscow while Fiorentina await AS Roma, with return legs to be played a week later.
The 21-year-old Lukaku is top scorer remaining in the competition with six goals, mainly thanks to his hat-trick in the away leg and brace at home during Everton's 7-2 aggregate thumping of Swiss side Young Boys in the last round.
"Sometimes you need to remember the age he is, yet he is such a mature goalscorer," said his coach Roberto Martinez, whose side have won three of their four European home ties but who lie 14th in the Premier League.
The last time Everton got this far in Europe was 2007/08, when they lost on penalties to Fiorentina, but there is hunger in Everton's attitude that sees them targeting the final in Warsaw on May 27.
Everton's other Belgian, the 27-year-old winger Kevin Mirallas, who has three goals and an assist in the competition himself, feels the club's fans can boost them with their big European match mentality.
"The away game will be difficult because of the stadium and the atmosphere," Mirallas told the Everton FC website
"In Wolfsburg, Lille, Krasnodar and Bern, the fans came and it was great for the team," said Mirallas in reference to fan support against Everton's Europa League opponents so far.
Everton have been allocated 1,500 tickets for the game, priced at just one pound each, for a fan brave enough to travel after watching French fans threatened in Kiev when Guingamp lost there in the last round.
A group of some 300 Dynamo Kiev fans had come down pitchside and menacingly approached a small group of about 30 Guingamp fans who had made the trip from Brittany.
"The first game is at Goodison and that is the most important," said Mirallas
"If we can win 2-0 it will be good."
Everton are the Premier League's last team in the tournament after Liverpool were beaten on penalties by Besiktas and Tottenham lost to Fiorentina in the last round.
Dynamo coach Sergey Rebrov, who once played alongside Andriy Shevchenko for the club, also scored a brace at Everton in his playing days with Tottenham.
With two away wins in the Europa League Dynamo can count on their striker Andriy Yarmolenko, who has three goals so far in the competition.
Unbeaten in the competition this season, Inter are one of five Italian sides in the last 16, but they face a tough challenge against Wolfsburg who have not conceded a goal in their last three European games and are second in the Bundesliga.
Inter have won the competition three times already with successes in 1991, 1994 and 1998.
Roma beat Fiorentina 2-0 at home in Serie A this season and drew 1-1 away which will mean Rudi Garcia's side will feel confident after winning their last away game in Europe too.
Holders Sevilla travel to free-scoring Villareal for the battle of La Liga hopefuls
The hosts have scored 20 goals so far in the Europa league
Dynamo Moscow are in Napoli, knowing their rivals on the night have kept five consecutive clean sheets.
Napoli coach Rafael BenÃÂtez has won the competition twice previously in 2004 with Valencia and in 2013 with Chelsea, the last English winners of the trophy.
Fixtures
Thursday
Zenit v Torino 1700 GMT
Wolfsburg v Inter Milan, Dnipro v Ajax, Clubb Brugge v Besiktas (all 1900 GMT)
Fiorentina v Roma, Everton v Dynamo Kiev, Villareal v Seville, Napoli v Dynamo Moscow (all 2005 GMT)
Source : AFP
Source: AFP